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Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by applying a randomized algorithm to the original data, which introduces unique challenges in data analysis by distorting inherent patterns. In particular, causal inference using observational data while preserving privacy is challenging…

含噪声充分统计量下的最优政策AI 解读

We study how policy-makers should set $k$ policy instruments so as to best hit $m$ (perhaps dynamic) targets, in a linear-quadratic model where there is statistical uncertainty about the causal effects of the policies. Plugging the estimated effects into "sufficient statistics" optimal policy formulas, as commonly done in the literature, can result in infinite risk. In fact, maintaining the status quo regardless of the data is uniquely minimax-optimal when $m>1$, and…

全维高斯混合模型 NPMLE 的自正则化与结构自适应AI 解读

We establish structural properties of the nonparametric maximum likelihood estimator (NPMLE) for $d$-dimensional Gaussian mixtures whose means lie in a hypercube. We show that, with high probability, the NPMLE based on $n$ independent observations self-regularizes by fitting a mixture model with $O((\frac{\log n}{\log\log n})^d)$ components, achieving the optimal model complexity without explicit model selection. Furthermore, the NPMLE exhibits a structural adaptation…

随机块模型中的率最优谱似然比聚类AI 解读

Spectral clustering commonly assigns communities by clustering a low-dimensional representation, whereas likelihood refinement can improve an initial assignment using the observed edges. We ask whether sharp community-recovery accuracy can be retained when the refinement no longer accesses individual edges. We develop spectral likelihood-ratio clustering for stochastic block models using one regularized adjacency eigensystem and the original vertex degrees. The method…

可交换收缩过程先验下稀疏贝叶斯因子模型的弱因子恢复AI 解读

Sparse Bayesian factor models provide a flexible framework for learning low-dimensional latent structure in multivariate data, but inference on the number of active factors remains challenging when some factors are weak or highly sparse. We study weak factor recovery under a variance based exchangeable shrinkage process (ESP) prior. We derive the posterior factor activation mechanism and show that, conditional on the global and local shrinkage parameters, activation is…

从高频期权价格对 Bergomi 模型的边际复合似然估计AI 解读

We develop a theory for estimating the kernel parameters of Bergomi-type stochastic volatility models from option-price time series. The framework allows positive kernels that may be singular at the origin, including the pure power-law kernel of the rough Bergomi model. Using the option-price representation of cumulative forward variance, we formulate the statistical experiment as exact observations of this quantity on increasingly fine time-maturity grids over a fixed…

Model combination offers an alternative to selecting a single forecasting model, particularly when individual models are sensitive to random initialization and hyperparameter choices. We study online aggregation through Follow-the-Leader (FTL) and Hedge-type algorithms, with an application to ensembles of Multi-Frequency Echo State Networks (MFESNs) for macroeconomic forecasting. On the theoretical side, we derive Hoeffding- and Bernstein-type expected-regret bounds for FTL…

I develop asymptotic theory for Granular Instrumental Variables (GIV) in large panels with both cross-section ($N$) and sample size ($T$) growing. The granular instrument is constructed from individual shocks that must be estimated from the panel. I show that this estimation has a first-order effect on the asymptotic variance of the GIV estimator. Existing methods do not account for this effect, leading to incorrect standard errors and invalid inference. I derive corrected…

多源协变量偏移下高维非参数回归的最优神经估计AI 解读

We study high-dimensional nonparametric regression under multisource covariate shift, where $\mathrm J$ sources of training data share a common regression function but differ in their covariate distributions, sample sizes, and noise variances. Our goal is to combine these sources to estimate the regression function accurately under a target covariate distribution. We propose an oracle weighted neural estimator and establish its minimax optimality up to logarithmic factors…

用循环神经网络预测自回归非因果过程AI 解读

This paper examines the use of recurrent neural networks and their extensions for forecasting autoregressive causal-noncausal processes, characterized by local explosive patterns such as bubbles and spikes. We study the recurrent neural networks (RNN), long short-term memory networks (LSTM), gated recurrent unit (GRU), bidirectional LSTM, and also a simple feed-forward network (FNN) to reveal the difficulty of forecasting extreme values depending on the type of network and…

协整回归变量：折叠凹惩罚何时超越 LASSOAI 解读

LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we…

稀疏面板数据的同质性追踪AI 解读

In panel data analysis, studying individual attributes is important for both methodological development and practical applications. Homogeneity in individual attributes and sparsity in coefficients are therefore important topics, as they help uncover relationships among individuals and identify the truly relevant covariates. However, many existing approaches do not explicitly exploit the potential grouping information contained in separately fitted individual-level penalized…

平滑阈值 GARCH：拟极大似然估计与经验证据AI 解读

It is well established that the volatility of daily stock returns responds asymmetrically to news, as described by the news impact curve (NIC), which relates volatility to the previous return. Empirical studies suggest that (i) volatility reacts more strongly to negative returns than to positive returns of the same magnitude, (ii) the point of asymmetry, where the NIC attains its minimum, is positive, and (iii) returns above this point often do not increase volatility at…

双重差分法之间差异有多大？一项大规模元分析AI 解读

I use AI-assisted replication to assess the empirical importance of negative weights in two-way fixed effects (TWFE) estimation, drawing on 1,346 staggered-adoption specifications from 108 economics papers. TWFE estimates are highly correlated with estimates from modern difference-in-differences methods, with observed sign reversals in 10.8-14.5% of comparisons and greater precision for TWFE. Hierarchical models that account for estimation noise imply a 91-98% correlation…

含近单位根阈值变量的阈值回归AI 解读

This paper considers threshold regression with an integrated or local-to-unity threshold variable and a threshold fixed in levels. We study the least squares threshold estimator and establish its asymptotic theory under both fixed and diminishing threshold effects. Under a fixed effect, the threshold estimator has a compound Cox argmin limit, whereas under a diminishing effect, its limiting distribution is characterized by a two-sided Brownian argmax with a random scale. We…

福利风险：政策评价的分布稳健界AI 解读

This paper develops a framework to study how the welfare effects of policy interventions are distributed across individuals when those effects are not directly observed. We bound the superquantile of individual welfare changes by the superquantile of conditional average welfare changes, which is typically identified, revealing how gains and losses are spread across the population. We also bound the share of the population whose welfare loss from the policy exceeds any given…

We develop methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. We define scenarios through distributional restrictions on observables, structural shocks and idiosyncratic components. The…

连续处理因果推断中的非线性充分降维AI 解读

Causal inference with continuous treatments requires estimating nuisance functions to adjust for the potentially high-dimensional confounder, but nonparametric estimation of these functions is severely hampered by the curse of dimensionality. To address this challenge, we propose a nonlinear sufficient dimension reduction framework to construct low-dimensional sufficient confounders to preserve the unbiasedness of the treatment effect. We estimate the causal effect by…

We study the functional average treatment effect on the treated in a two-period difference-in-differences design. Under conditional functional parallel trends, we derive the full-curve efficient influence function and efficiency bound and construct a cross-fitted, doubly robust estimator. Under ultra-dense observation, bounds on curve-estimation error and learner stability preserve its full-data first-order behavior. Nuisance-rate and moment conditions yield asymptotic…

We establish a functional central limit theorem for locally stationary time series in a separable Banach space $B$. The result requires no type-2 or cotype assumptions and thus covers spaces central to functional data analysis, such as $C([0,1])$ and $L^p([0,1])$. Under moment conditions, summable physical dependence coefficients and a bracketing entropy condition controlling the infinite-dimensional tails, the centered partial sum process converges weakly in $D([0,1],B)$ to…

非平稳下仍保持枢轴性的自归一化变点检验AI 解读

Self-normalising test statistics for time series circumvent the lag-specification of long-run variance estimators by employing an inconsistent estimator for studentization. This leads to asymptotically pivotal test distributions under stationarity, but not for nonstationary sequences. Focusing on the multiple changepoint problem, we propose an alternative self-normalised test statistic which is asymptotically pivotal even if the noise is nonstationary. Central to our…

多元计数时间序列的稀疏有向网络恢复AI 解读

Count time series arise naturally in many scientific applications. Examples include species abundances collected over time, and gene expression counts over pseudotime. Network inference from such data can yield important insight into underlying biological mechanisms, but is challenging because count observations are discrete, overdispersed, and temporally dependent. We propose a multivariate Poisson log-normal model in which observed counts arise from a Poisson distribution…

零补外推：秩亏与极端不平衡下的逻辑回归参数恢复与分类AI 解读

Parameter estimation and classification in binary logistic regression deteriorate severely when the number of minority class observations ($n_1$) is smaller than the feature dimension ($p$). Under such rank-deficient rarity ($n_1 < p$), maximum likelihood estimators suffer from quasi-complete separation, penalized likelihood methods exhibit severe intercept bias, and convex minority oversampling techniques such as SMOTE collapse into an $(n_1 - 1)$-dimensional affine…

独立可学习性的谱边界AI 解读

Learning independence is fundamental to statistical inference and machine learning, yet learning independence between entire time series by a test remains challenging when only a single observation record is available. Existing guarantees often rely on structural or mixing assumptions, while stationarity and ergodicity alone do not permit consistent testing. In this work, we identify a class-level boundary governed by shared nontrivial Koopman eigenvalues, which represent…